1. Field of the Invention
The present invention relates to an accelerometer and, more particularly, to a pendulous accelerometer that includes a pendulum or proof mass coupled to an isolator by way of a plurality of flexures and resonators; the isolator, in turn, coupled to a support by way of a plurality of flexures in order to reduce cross coupling errors in the accelerometer output which result from the cross axis sensitivity of the pendulum.
2. Description of the Prior Art
Pendulous accelerometers are generally known in the art. Examples of such accelerometers are disclosed in U.S. Pat. Nos. 5,005,413 and 5,287,744, hereby incorporated by reference. Such pendulous accelerometers, particularly open-looped pendulous accelerometers with finite elastic compliance, are subject to cross coupling errors resulting from the cross axis sensitivity of the pendulum. This cross coupling error is best understood with reference to FIG. 1 which illustrates a pendulous accelerometer 20 which includes a proof mass or pendulum 22 coupled to a fixed support 24 by way of a flexure 26. The flexure 26 enables the pendulum 22 to rotate about a hinge axis HA; perpendicular to the plane of the page. Movement of the proof mass 22 is constrained by way of a pair of resonators 28 and 30, for example, double-ended tuning forks (DETFs). With such a configuration, accelerations applied along the positive input axis a.sub.I cause the proof mass 22 to deflect downwardly which, in turn, causes tension and compression forces in the resonators 28 and 30, respectively. The deflection of the proof mass 22 resulting from an acceleration applied along the input axis a.sub.I thus changes the direction of the input axis a.sub.I and, hence, causes a proportional sensitivity to acceleration applied along a pendulous axis a.sub.P, generally normal to the input axis a.sub.I. More particularly, the downward deflection of the proof mass 22 resulting from accelerations applied along the input axis a.sub.I enables accelerations or components along the pendulous axis a.sub.P to produce a torque which rotates the proof mass 22 down further, thus increasing the forces applied to the resonators 28 and 30. As such, the cross axis sensitivity of the proof mass introduces an error term in the accelerometer 20 output given by equation 1 below. EQU E=K.sub.ip *a.sub.I *a.sub.P, (1)
where K.sub.ip is a cross coupling error coefficient; a positive constant for the conditions described above; a.sub.I =acceleration relative to the input axis a.sub.I and a.sub.P =acceleration relative to the pendulous axis a.sub.P.
This cross coupling error is undesirable because it can produce static errors comparable to bias errors in an inertial grade accelerometer and because synchronous vibration along the input and pendulous axis a.sub.I and a.sub.P simultaneously will rectify to produce a dc error without a dc input. As such, various attempts have been made to compensate for such cross coupling errors, as illustrated in FIGS. 2-4. FIG. 2 illustrates a known accelerometer 32 which includes a pair of proof masses 34 and 36, connected to supports 38 and 40 by way of flexures 42 and 44, respectively. Each proof mass 34, 36 is connected to its respective support 38, 40 by way of a resonator 46 or 48. With the configuration as shown, the pendulum 36 produces a cross coupling error which is of opposite sign of the cross coupling error produced by the pendulum 34 when the outputs of the resonators 46 and 48 are combined in such a way to cause the responses to an acceleration along the input axis a.sub.I to reinforce. However, in order for the cross coupling errors to cancel completely, the pendulums 34, 36 must be matched for natural frequency and damping which increases the fabrication cost and space requirements. In addition, the embodiment illustrated in FIG. 2 is relatively large and heavy and requires two precision flexures.
FIG. 3 illustrates another known accelerometer 50 that is relatively smaller and less complex than the accelerometer 20 which also includes means for compensating the cross coupling error. The accelerometer 50 includes a pendulum or proof mass 52 coupled to a fixed support 54 by way of a flexure 56. Rotation of the proof mass 52 is constrained by way of a pair of resonators 58 and 59. Since the resonators 58 and 59 are made from different material than the pendulum 52, the resonators 58 and 59 are coupled to a thermal isolator 57 to compensate for thermal stresses. The thermal isolator 57, in turn, is coupled to a support 60 and configured to be highly compliant for translation parallel to the pendulous axis a.sub.P but stiff for rotation about an axis generally parallel to the hinge axis (i.e., an axis perpendicular to the plane of the page) to relieve thermal stress. The isolator 57 is positioned such that accelerations parallel to the pendulous axis a.sub.P places both the resonators 58 and 59 in either tension or compression at the same time, while accelerations applied along the input axis a.sub.I puts one resonator 58 or 59 in tension and the other in compression. Since the output of the resonators 58 or 59 is known to be nonlinear, these sensitivities can be tuned to produce a pseudo-K.sub.ip which cancels the cross coupling error coefficient K.sub.ip.
However, there are several drawbacks with the accelerometer 50. First, the cross coupling error coefficient K.sub.ip is dependent upon a comparatively large nonlinear coefficient K.sub.ii, inherent in the resonators. Since the coefficient K.sub.ii can be affected by the data processing, the configuration can only provide acceptable results as long as the mechanical designer controls both the sensor design and the data processing. A second drawback of the accelerometer 50 is that it uses resonators 58 and 59 on the top and bottom of the pendulum 52; contrary to the current trend in silicon sensor fabrication in which both of the resonators are formed in one plane for easier fabrication and to obviate the need to depend on two matched epitaxial layers. Lastly, the thermal isolator 57 is basically unnecessary in monolithic silicon designs since the structure is made of an essentially homogeneous material, for example, as disclosed in U.S. Pat. No. 5,005,413.